After a meeting with President Barack Obama in the West Wing along with Senator Lindsey Graham, Senator John McCain said Monday that the failure of Obama’s request for authorization to strike Syrian President Bashar Assad’s regime in response to the use of chemical weapons “would be catastrophic” for the U.S.

Speaking to reporters outside the White House, McCain and Graham said they are not yet a lock to vote for the measure, saying they want to see Obama articulate a broader strategy for what happens when the cruise missiles stop falling to turn the tide of Syria’s civil war in favor of the opposition.

“Now that a resolution is going to be before the Congress of the United States, we want to work to make that resolution something that majorities of the members of both houses could support,” McCain said. “A rejection of that, a vote against the resolution by Congress, I think would be catastrophic, because it would undermine the credibility of the United States of America and of the President of the United States. None of us want that. What we do want is an articulation of a goal that over time to degrade Bashar Assad’s capabilities, increase and upgrade the capabilities of the Free Syrian Army and the Free Syrian government so they can reverse the momentum on the battlefield.”

McCain said he encouraged Obama to think beyond simply punitive strikes against Assad, saying, “A weak response is almost as bad as doing nothing.” After the meeting, he declined to discuss the options Obama laid out, but said a larger response is now under consideration. “I don’t think it’s an accident that the aircraft carrier is moving over in the region,” he said.

McCain called it “shameful” that the Administration has not stepped up its military assistance to the opposition, criticizing Obama’s efforts over the past two years as “a policy of neglect,” but the lawmakers signaled that may change. “There seems to be emerging from this Administration a pretty solid plan to upgrade the opposition, to get the regional players more involved,” Graham said. “We still have significant concerns, but we believed there is in formulation a strategy to upgrade the capabilities of the Free Syrian Army and degrade the capabilities of Bashar Assad,” McCain added. “Before this meeting we had not had that indication.”

McCain and Graham said Americans and their fellow members of Congress need to understand that the conflict in Syria is not an isolated civil war but a “regional conflict.”

“I can’t sell another Iraq or Afghanistan, because I don’t want to,” Graham said, previewing his messaging to his constituents as well as to his colleagues. “I can sell to the people of South Carolina that if we don’t get Syria right, Iran is surely going to take the signals that we don’t care about their nuclear program, and it weighs on the President’s mind strongly about the signals we send. So if we lost a vote in the Congress dealing with the chemical weapons being used in Syria, what effect would that have on Iran in terms of their nuclear program? Most South Carolinians get that point.”

The meeting was the latest effort by the Obama Administration to build support in Congress for intervention in Syria. The lawmakers said the Administration still has its work cut out for it in the days ahead.

“I am already talking to a lot of my colleagues, but before I can persuade them to support this, I have to be persuaded,” McCain said.